Equalization is the process of reducing the effects of distortion over signal transmission paths by compensating for the signal path distortion at either or both ends of the transmission medium. A training sequence may be employed to adapt an equalizer to compensate for the signal path distortion, which may alter the amplitude and/or phase of a signal.
For phase- and amplitude-modulated transmission schemes, the phase and amplitude of a signal are selectively shifted to combinations of values, each combination representing a different set of transmitted bits, commonly referred to as "symbols." At a receiver, proper decoding of the transmitted symbols requires detection of the various combinations of phase and amplitude. For two-dimensional modulation schemes, the signal is represented mathematically by an in-phase ("I") component and a quadrature-phase ("Q") component, which are separated by a phase difference of .pi./2. A two-dimensional plot of the I and Q components for a complete set of received symbols produces a pattern referred to as a constellation.
Because of signal path distortion, the proper detection of the I and Q components of a signal can be difficult to obtain. One source of interference is intersymbol interference which results when consecutively-transmitted symbols interfere with one another. To compensate for intersymbol interference ("ISI"), especially in bandwidth-efficient communication receivers that operate with a data rate close to the channel capacity, an equalizer that uses a fractionally-spaced adaptive filter may be used, as described in S. U. H. Qureshi, "Adaptive Equalization," Proceedings of IEEE, v.73, No. 9, pp. 1349-87 (1985), which is incorporated by reference as if fully set forth herein. An adaptive filter can modify the filter coefficients, or "tap weights," used by the filter to remove ISI. Updating of the filter coefficients is done to minimize an error at the output of the filter, which is effectively a measure of the difference between the actual output of the filter and the expected output. The adaptive process continues until the error signal is at a minimum, which indicates that the filter has "converged." The convergence of an equalizer depends on many factors, e.g., the initial filter coefficients, signal-to-noise ("SNR") ratio, and phase changes caused by clock recovery at the receiver, but can be accomplished using various adaptive algorithms, such as the conventional Least Mean Square ("LMS"), Reduced Constellation Algorithm ("RCA"), or the Constant Modulus Algorithm ("CMA"). RCA is described by Benveniste and Goursat in "Blind Equalizers," IEEE T. Comm., v. 32, no. 8, pp. 871-883, August 1984, and CMA is described by Godard in "Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems," IEEE T. Comm., v. 28, no. 11, pp. 1867-1875, November 1980, both of which are incorporated herein by reference, as if reproduced in their entirety.
The adaptation of the filter coefficients in an adaptive equalizer is based on an assumption that a correct decision is made regarding which symbol is received at a given time. The assumption is valid for equalizers using a training sequence for which the identity of each received signal is known a priori. Some equalizers, however, are also used without the benefit of a training sequence, in which case the assumption is not necessarily correct; such equalizers are commonly referred to as "blind" equalizers, implying a possibility that the filter coefficients may be erroneously updated. Although the possibility of a mistake exists, if a blind equalizer makes correct decisions for a sufficiently-large set of received symbols, the equalizer will converge.
Fractionally-spaced equalizers are generally insensitive to sampling phase; the basic reason for insensitivity due to the capability of fractionally-spaced equalizers to introduce an arbitrary delay, or "phase shift," from the input to the output. For some schemes, a rotator/derotator may be used to correct for this phase shift. The use of a rotator/derotator, however, adds additional complexity and cost to a device. Therefore, there is a need in the art for an equalization scheme that does not require the use of a rotator/derotator to correct for phase shift, or phase "error," in devices employing fractionally-spaced adaptive equalizers.